21. Olivier Lessmann At Logic And It's Applications In Algebra And Geometry, Ann Arb algebraically closed fields of a given characteristic, and free groups are threeexamples of classes of mathematical structures which are categorical in all http://www.math.lsa.umich.edu/~bkasterm/OlivierLessmann.html

Olivier Lessmann. Dimension theory in model theory. Vector spaces, say over the rationals, algebraically closed fields of a given characteristic, and free groups are three examples of classes of mathematical structures which are categorical in all uncountable cardinals, i.e. any two uncountable such structures of the same size are isomorphic. In each of these instances, there is a notion of dimension (linear dimension, transcendence degree, the number of generators) which captures the isomorphism-type of the structure. This is a general model-theoretic phenomenon: Th: (Lessmann) If K is a reasonable class of mathematical structures which is categorical in some uncountable cardinal, then inside each mathematical structure there is a pregeometry whose dimension determines the isomorphism-type of the mathematical structure, and furthermore, the class is categorical in all uncountable cardinals. By reasonable, we mean (1) axiomatised using at most countably many first order axioms (the first two examples above, in this case this is the classical Baldwin-Lachlan theorem), or, more generally, (2) axiomatised using not necessarily first order axioms but in such a way that there is a good notion of universal domain (a homogeneous model as in the example of free groups, or a full model). The difficulty in (2) is that the compactness theorem fails. The use of dimension theory to understand mathematical structures works beyond can categoricity: Inside any mathematical structure, we can define what we mean by "A is independent from B (over C)" using the automorphism group of the structure. This independence relation has good properties under very general model-theoretic circumstances, called simplicity and stability (shown by Buechler-Lessmann). Examples of stable and simple mathematical structures are those described above (in each case the independence relation becomes the familiar one: in vector spaces it becomes linear independence, and alebraic independence in an algebraically closed field), as well as Hilbert spaces, where the independence relation coincides with orthogonality.

22. Monica VanDieren At Logic And It's Applications In Algebra And Geometry, Ann Arb Tame classes include (but are not limited to) homogeneous classes, excellentclasses, categorical AECs with amalgamation and good frames. http://www.math.lsa.umich.edu/~bkasterm/MonicaVanDieren.html

Monica VanDieren. Stability in Tame AECs. This is joint work with Rami Grossberg. Homepage of speaker: http://math.stanford.edu/~monica/home.html

23. Logic And Foundations Of Programming At QMW Department of Computer Science, logic and Foundations of Programming group. Members, research projects.Category Science Math Institutions Europe United Kingdom...... type theory and its semantics; operational semantics; foundations of logic programming.Semantics Universal algebra; category theory; categorical model theory http://www.dcs.qmw.ac.uk/research/theory/

Logic and Foundations of Programming The LFP group is one of six research groups here in the Department of Computer Science at Queen Mary University of London The group organises joint theory seminars together with the Theory and Formal Methods Group at Imperial College. We meet for lunch on Wednesdays at one O'clock in room CS/446 above the Student Union shop. Visitors are welcome to attend and join in with our informal presentations and discussions of our current research. There's an incomplete list of lunches. The Department is the site for Hypatia , a directory of research workers in Computer Science and Pure Mathematics and a library of their papers. This document has sections on the group's People Projects and Research People Faculty and Research Staff Richard Bornat richard@dcs.qmw.ac.uk Peter Burton peterb@dcs.qmw.ac.uk ... graham@dcs.qmw.ac.uk Research Students Pablo Armelin pablo@dcs.qmw.ac.uk Jules Bean jules@dcs.qmw.ac.uk ... mikes@dcs.qmw.ac.uk Former members David Pym pym@dcs.qmw.ac.uk ), now at Bath Samin Ishtiaq si@dcs.qmw.ac.uk ), now at ARM Ltd Paul Blain Levy pbl@dcs.qmw.ac.uk

24. Information And Computation -- 1995 A process algebra for timed systems. GL McColm. Pebble games and subroutines inleast fixed point logic. A categorical linear framework for Petri nets. http://theory.lcs.mit.edu/~iandc/ic95.html

Information and Computation 1995 Volume 116, Number 1, January 1995 Michiel Smid . Dynamic rectangular point location with an application to the closest pair problem. Information and Computation , 116(1):1-9, January 1995. Abstract, References, and Citations. BibTeX entry Michael Huth . A maximal monoidal closed category of distributive algebraic domains. Information and Computation , 116(1):10-25, January 1995. Abstract, References, and Citations. BibTeX entry Juanito Camilleri and Glynn Winskel . CCS with priority choice. Information and Computation , 116(1):26-37, January 1995. Abstract, References, and Citations. BibTeX entry Bent Thomsen . A theory of higher order communicating systems. Information and Computation , 116(1):38-57, January 1995. Abstract, References, and Citations. BibTeX entry Anil Nerode Raymond T. Ng , and V. S. Subrahmanian . Computing circumscriptive databases: I. Theory and algorithms. Information and Computation , 116(1):58-80, January 1995. Abstract, References, and Citations. BibTeX entry Naoki Abe . Characterizing PAC-learnability of semilinear sets. Information and Computation , 116(1):81-102, January 1995.

25. Cours Functoriality. Naturality. Monoidal categories. categorical logic. Hopf algebra.Linear logic. MAT3341, Applied Linear algebra Vector and matrix norms. http://aix1.uottawa.ca/~epaqu045/cours.html

Cours Suivis Directed studies: Quantum Groups Hopf algebra. Quantum plane and its symmetries. The lie algebra SL(2). The enveloping of sl (2). Hopf algebra Structure on U q sl (2)). Yang-Baxter equation and (co)braided bialgebras. Drinfeld's quantum double. Serminar: Quantum Computing Basics of quantum mechanics. Quantum states. Quantum entanglement and decoherence. Classical and quantum information theory. Quantum computations. Quantum cryptography. Shor's algorithm for fast factorisation. Mathematical Logic Propositional and predicate logic. Syntax and semantics of formal systems. Saturation theorems. Incompleteness and undecidability theorems. Special topics in mathematics: Introduction to category theory and categorical logic Introduction to category theory. Functoriality. Naturality. Monoidal categories. Categorical logic. Hopf algebra. Linear logic. Applied Linear Algebra Vector and matrix norms. Schur canonical form, QR, LU, Cholesky and singular value decomposition, generalized inverses, Jordan form, Cayley-Hamilton theorem, matrix analysis and matrix exponentials, eigenvalue estimation and the Greshgorin Circle Theorem; quadratic forms, Rayleigh and minima principles. The theoretical and numerical aspects will be studied.

26. FOM: The Categorical Approach To Logic The context was my point that algebra is not the same as logic, and that the algebraicor categorical approach to logic omits a lot of important information http://www.cs.nyu.edu/pipermail/fom/1998-April/001837.html

FOM: the categorical approach to logic Stephen G Simpson simpson@math.psu.edu Wed, 1 Apr 1998 10:39:56 -0500 (EST) Previous message: FOM: history and f.o.m. Next message: FOM: the categorical approach to logic Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: history and f.o.m. Next message: FOM: the categorical approach to logic Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

27. Gnist.no: Fagbokhandelen På Internett Rosebrugh, R. Sets for Mathematics categorical algebra is used the study of geometry,analysis, and algebra. Analysis and logic Articles from four researchers http://www.gnist.no/kategori.php?kategori=PBC

28. A Reflective Module Algebra With Applications To The Maude Language structured theories in a categorical way and giving some useful results for them.As a first step towards a generic module algebra in a framework logic such as http://maude.cs.uiuc.edu/papers/abstract/Dmodalg_1999.html

A Reflective Module Algebra with Applications to the Maude Language Introduction It has long been recognized that large specifications are unmanageable unless they are built in a structured fashion from smaller specifications using specification-building operations. Modularity and module composition are central notions for specification languages and declarative programming languages. Although Parnas is the author of the possibly earliest work on software modules, Burstall and Goguen were the first to study the semantics of modular specifications and their composition operations in their language Clear. They proposed the idea of ``putting theories together'' by composing them through operations having a clean and logic-independent categorical semantics. Continuing in this line of work, Burstall and Goguen captured the minimal requirements that a logic must meet to be a reasonable specification framework and introduced the notion of institution Categorical techniques have allowed since then the study of specification-building operations with independence of any specific formalism by different authors, giving rise to a large body of research. Algebraic specification is now a mature field of Computer Science because of its mathematical foundations. After Clear, the theory of algebraic specification has been implemented in many computing systems, such as OBJ, ACT ONE, ASL, ASF, PLUSS, LPG, Larch, CASL, etc., and has become an important technique in software engineering methodologies.

29. Category Theory F. Borceux, Handbook of categorical algebra 13. GM Kelly, Basic Concepts ofEnriched Category Theory. Topos Theory. categorical logic and Type Theory. http://www.kyoto-su.ac.jp/~hxm/categorical/ct/

$B7wO@!J(BCategory Theory$B!K(B $B7wO@$K4X$9$k%a%b!%$^$@:n$j$+$1$G$9!%(B Books Basic and Advanced Texts S. Mac Lane, Categories for the Working Mathematician. F. Borceux, Handbook of Categorical Algebra 1-3. G. M. Kelly, Basic Concepts of Enriched Category Theory. Topos Theory S. Mac Lane and I. Moerdijk, ... M. Barr and C. Wells, Toposes, Triples and Theories P. Johnstone, Topos Theory P. Johnstone, Stone Space Categorical Logic and Type Theory J. Lambek and P. J. Scott, Introduction to Higher Order Categorical Logic. B. Jacobs, Categorical Type Theory. A. Torelstra, Lectures on Linear Logic M. Makkai and G. Reyes, ... Categorical Model Theory and Varieties J. Adamek and J. Rosicky, ... LNM, Computer Science J. Mitchell, Semantics of Programming Language C. Gunter, Semantics of Programming Language G. Winskel, Semantics of Programming Language J. Reynolds, Semantics of Programming Language M. Barr and C. Wells, Category Theory for Computing Science Synthetic Differential Geometory Models of Infinitesimal Analysis Basic Concepts of Synthetic Differential Geometory J. L. Bell, ...

30. Logic - CASE Bibliography On Rigid Structures. Journal of Symbolic logic, vol. Eilenberg, S., Harrison, DK,Mac Lane, S., and Roehrl, H., editors, categorical algebra, pages 120. http://david_hewins.tripod.com/papers/id13.html

Get Four DVDs for $.49 each. Join now. Tell me when this page is updated Papers Logic - CASE Bibliography HOME Aristotle BOOK Cherokee ... Logic - CASE Logic - CASE Bibliography Moon PETS Security September ... Archives Logic - CASE Bibliography: Articles and URLs. Ajtai, M. and Y. Gurevich (1987). Monotone versus positive. J. of ACM, 34, 1987, 1004-1015. Atzeni, Paolo and Peter P. Chen (1981). Completeness of Query Languages for the Entity-Relationship Model. Entity-Relationship Approach to Information Modeling and Analysis, ed. P.P. Chen. ER Institute, 1981. Republished in Second International Conference on the Entity-Relationship Approach, 1981 (1983). North-Holland. Bachman, Charles (1991). CASE Trends Interviews Charles Bachman. In CASE Trends, Summer 1991, p. 31f. Software Productivity Group, Shrewsbury, MA Baldwin, J.T. (1985). Classification Theory: 1985. In Baldwin, 1985-2, pp. 1-23. Baldwin, J.T. and Joel Berman (1985). Concrete Representations of Lattices and the Fundamental Order. In Baldwin, 1985-2, pp. 24-31. Blass, Andreas and Yuri Gurevich (1987). Existential fixed-point logic. Logic and complexity (ed. E. Börger). Springer Lecture Notes in Computer Science volume 270, 1987, 20-36.

31. The Unwritten Book logic. Introduction To Boolean algebra; Dialog logic Felscher'sRules; The Definition Of logic, Sequents and categorical algebra; http://www.uwm.edu/~whopkins/logic/

Logic Introduction To Boolean Algebra Dialog Logic Felscher's Rules The Definition Of Logic, Sequents and Categorical Algebra Rules Of Logic (Cheat Sheet) ... The Unwritten Book

32. 5 De Morgan's Life And Work Figure 2 De Morgan's notation for the categorical forms AOEI. Besides his workin algebra and logic, De Morgan contributed 712 articles to the ``Penny http://www.hf.uio.no/filosofi/njpl/vol2no1/history/node5.html

Next: 6 Boole's Life Up: A Brief History of Previous: 4 British Mathematics in 5 De Morgan's Life and Work Augustus de Morgan was born as fifth child on the 27th of June 1806 in Madura, India, where his father worked as an officer for the East India Company. His family soon moved to England, where they lived first at Worcester and then at Taunton. His early education was in private schools, where he enjoyed a classic education in Latin, Greek, Hebrew, and mathematics. In 1823, at the age of 16, he entered Trinity College in Cambridge, where the work of the ``Analytical Society'' had already changed the students' schedule so that De Morgan also studied Continental mathematics. In 1826, he graduated as a fourth Wrangler and turned his back on mathematics to study to be a lawyer at Lincoln's Inn in London. But only a year later he revised this decision and applied for a position as professor of mathematics at the newly established University College in London. At the age of 22, with no publications, he was appointed. The work that De Morgan produced in the years to come spanned a wide variety of subjects with an emphasis on algebra and logic. But surprisingly he was not able to connect them. An important work of his was the ``Elements of Arithmetic'', published in 1830, containing a simple yet thorough philosophical treatment of the ideas of number and magnitude. In a paper from 1838 he formally described the concept of mathematical induction and in 1849 in ``Trigonometry and Double Algebra'' he gave a geometrical interpretation of complex numbers.

33. Bilgi Mathematics Faculty: Prof. Oleg Belegradek 4, 37. On almost categorical theories, Sibirsk. Finitely approximable associativealgebra with unsolvable word problem, algebra and Logika 39, no. logic 65, no http://math.bilgi.edu.tr/people/belegradek/

Prof. Oleg Belegradek Faculty Students Alumni Poizat's Model Theory Book in Russian CURRICULUM VITAE for Oleg Belegradek Date of birth November 24, 1949 Place of birth Chelyabinsk, Russia Telephone +90 (212) 2162222/198 (office) +90 (212) 2168477 (fax) e-mail address: olegb@bilgi.edu.tr Degrees Doctor of Science (Mathematics), 1995, Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Novosibirsk Candidate of Science (Mathematics), 1975, Novosibirsk State University Master (Mathematics), 1972, Novosibirsk State University Research areas Algebra, mathematical logic and applications Academic career Kemerovo State University, Department of Mathematics, Section of Algebra and Geometry, 1975-1977: Assistant professor, 1977-1986: Chairman, 1987-1995: Docent, 1995-1999: Professor Istanbul Bilgi University, Department of Mathematics, 1999-present: Professor Honours, awards, fellowships University of London, QMW College, 1992 Fields Institute, Toronto, 1996 MSRI, Berkeley, 1998

34. Category Theory dimensional categories; applications of category theory to algebra, geometry and scientificknowledge that make use of categorical methods logic and Philosophy. http://lgxserver.uniba.it/lei/logica/lgcat_th.htm

Related Pages Index HOME English HOME Italiano Category Theory Research / Miscellaneous Category Theory Il sito, curato da Luca Mauri , fornisce risorse e informazioni sulla teoria delle categorie e links a riviste su tale argomento e a numerose altre pagine. Reviews / On-Line Publications Theory and Applications of Categories "The journal Theory and Applications of Categories will disseminate articles that significantly advance the study of categorical algebra or methods, or that make significant new contributions to mathematical science using categorical methods. The scope of the journal includes: all areas of pure category theory, including higher dimensional categories; applications of category theory to algebra, geometry and topology and other areas of mathematics; applications of category theory to computer science, physics and other mathematical sciences; contributions to scientific knowledge that make use of categorical methods.". Il Journal  distribuito gratuitamente via WWW/ftp, dopo essersi registrati. Related Fields Foundations of Mathematics Logic and Philosophy Logic and Mathematics Logic and Computer Science General Resources SWIF Back to the Top Index HOME English ... HOME Italiano

35. Handbook Of Categorical Algebra 2 Categories And Structures Encyclopedia Of Math the Swan EB White Fred Marcellino Computer Science logic 5th Workshop Handbook ofCategorical algebra 2 Categories and Structures Encyclopedia of Mathematics http://www.freebookreview.com/Francis_Borceux_book_Handbook_of_Categorical_Algeb

More books : Lie Algebras Finite and Infinite Dimensional Lie Algebras Andapplications in Physics Studies in Mathematical Physics Vol 7 by E A Dekerf A P E Ten Kroode The Oxford Dictionary of the Christian Church written by E A Livingstone F L Cross Butterfly Giftwrap Paper 2 Sheets With 3 Matching Gift Cards book by E A Seguy Synthesis and Applications of Isotopically Labelled Compounds 1991 Proceedings of the Fourth International Symposium Toronto Canada 3 - 7 Septemb E Buncel GW Kabalka Computational Methods in Engineering Science E Arantes E Oliveira Biological Degradation of Organic Chemical Pollutants in Biofilm Systems E Arvin The Trumpet of the Swan E B White Fred Marcellino Computer Science Logic 5th Workshop Csl 91 Berne Switzerland October 7 - 11 1991 Proceedings Lecture Notes in Computer Science Vol 626 E Borger Psychologische Probleme in Der Reproduktionsmedizin Jahrbuch Der Medizinischen Psychologie Bd 5 E Brahler A Meyer Bautechnik Konstruktiver Ingenieurbau 3 Massiv - Und Stahlbau E Cziesielski What Your Second Grader Needs to Know Fundamentals of a Good Second Grade Education The Core Knowledge Series E D Hirsch Links zi Karmel Hazi Carmel book Intelligence for Peace The Role of In egory Cooper book Collectible Compact Disc Price Guide 2 2nd Edi no book Recent Advances in the Study of Hepatitis C Virus Interv orge L Trigg Edmund H Immergut book Magnetic Materials to Mechan ... Index Handbook of Categorical Algebra 2 Categories and Structures Encyclopedia of Mathematics and Its Applications Vol 51 by Francis Borceux

36. BIBLIOGRAPHY About DESCENT And CATEGORY THEORY! A. Obtu \book The logic of categories of partial book Introduction to categories,homological algebra, and sheaf Von Eye , et al \book categorical Variables in http://north.ecc.edu/alsani/catbib.html

BIBLIOGRAPHY about DESCENT THEORY from W. Tholen home page. Monades et Descente Selected Topics in Algebra An Outline of a Theory of Higher Dimensional Descent The Theory of Descent Triples and Descent An Extension of the Galois Theory of Grothendieck Theory of Categories over a Base Topos Descent Theory for Toposes Effective Descent Morphisms and Effective Equivalence Relations Introduction to Affine Group Schemes BIBLIOGRAPHY about CATEGORY THEORY F. W. Lawvere publications: http://www.acsu.buffalo.edu/~wlawvere Back to Descent and Category Theory WebPage Back to Alsani's home page

37. Atlas: Computable Isomorphisms Of Boolean Algebras With Operators By Bakhadyr M. Numerations, algebra and logic 19, N 5, p. 507551, 1980. 2 P. Cholak, SS Goncharov,B. Khoussainov, and RA Shore. Computably categorical structures and http://atlas-conferences.com/c/a/i/g/29.htm

Atlas Document # caig-29 International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures May 21-24, 2002 Vanderbilt University Nashville, Tennessee, USA Conference Organizers Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis and Matthew Valeriote View Abstracts Conference Homepage Computable Isomorphisms of Boolean Algebras with Operators presented by Bakhadyr M. Khoussainov Computer Science Department, The University of Auckland, New Zealand. joint research with Tomasz Kowalski (JAIST, Japan) In computable algebra and model theory computable isomorphism types of structures have been studied intensively over almost three decades. These include a number of natural classes of structures, such as Boolean algebras, Abelian groups, and lattices. The Handbook of Recursive Mathematics is a good source of results in the area. Here we present two results about computable isomorphisms of Boolean algebras with operators (BAOs). A computable BAO A is one whose domain is a computable subset of N, and whose Boolean operations and the operators are computable functions. If a BAO

38. Sources On The Philosophy Of Mathematics Mac Lane and Moerdijk, Sheaves in Geometry and logic , SpringerVerlag, 1992.Borceux, Handbook of categorical algebra (three volumes), Cambridge, 1994. http://www.rbjones.com/rbjpub/philos/maths/faq008.htm

Sources on: Several good collections of philosophical papers are available, e.g. and For material on logicism see the writings of Gottlöb Frege and those of Bertrand Russell Some good sources on intuitionism and constructive mathematics are Errett Bishop Douglas Bridges and Michael Beeson . For philosophical material relating to intuitionism Dummett must be mentioned (not withstanding his conspicuous absence from my bibliography). The "anti-foundationalist" heresy may be found in the works of Imre Lakatos Reuben Hersh and Phillip Davis and is copiously represented in . (see Are Foundations Necessary? for my affirmation of orthodoxy, though aimed a computer scientists rather than anti-foundationalists) On the more technical side provides a collection of important papers published in the first three decades of the 20th century. While predominantly by logicians this collection is a valuable resource for philosophers of mathematics. Each paper is prefaced by a contemporary overview and evaluation. There is a lot of material on the foundations of mathematics in the references above.

39. Listings Of The World Science Math Algebra Category Theory Post Review This site contains online books and research papers on the subjects ofcategorical algebra, categorical logic, categorical geometry, lattice theory http://listingsworld.com/Science/Math/Algebra/Category_Theory/

40. Bibliography Of G.Rosolini logic, 55, 1990. and Comput., 79, 1988. Rosolini, G. Representation theoremsfor special pcategories, In categorical algebra and its Applications, Ed. http://www.disi.unige.it/person/RosoliniG/biblio.html

Power, A. J., Rosolini, G. Fixpoint operators for domain equations Theoret. Comput. Sci. Carboni, A., Rosolini, G., Walters, R.F., editors Theory Appl. Categ. Robinson, E.P., Rosolini, G. An abstract look at realizability , In Computer Science Logic '01 , Ed. L. Fribourg , Lectures Notes in Computer Science, Fiore, M., Rosolini, G. Domains in H Theoret. Comput. Sci. Carboni, A., Rosolini, G. Locally cartesian closed exact completions J.Pure Appl. Alg. Rosolini, G. Equilogical spaces and filter spaces Rend. Circ. Mat. Palermo Rosolini, G. A note on Cauchy completeness for preorders Riv. Mat. Univ. Parma Rosolini, G. Sheaves Spring School on CATEGORICAL METHODS in LOGIC and COMPUTER SCIENCE Birkdedal, L., van Oosten, J., Rosolini, G., Scott, D. S., editors Workshop on Realizability Semantics and Applications , Elsevier Science, Electr. Notes in Theo. Comp. Sci., 1999 Rosolini, G., Streicher, Th. Comparing models of higher type computation , In Workshop on Realizability Semantics and Applications , Ed. Birkdedal, L., van Oosten, J., Rosolini, G., Scott, D. S., Elsevier Science, Electr. Notes in Theo. Comp. Sci., 1999 Birkedal, L., Carboni, A., Rosolini, G., Scott, D. S.

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